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The Impact of Bankruptcy Exemptions for Retirement Assets
Matthew C. Baker
Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in
partial fulfillment of the requirements for the degree of
Master of Science
In
Agricultural and Applied Economics
Hyrum Smith, Chair
George Davis
L. Leon Geyer
May 13, 2013
Blacksburg, VA
Keywords: Bankruptcy exemptions, financial planning, retirement assets, financial
sophistication, Heckman model
Copyright © 2013, Matthew C. Baker
The Impact of Bankruptcy Exemptions for Retirement Assets
Matthew C. Baker
ABSTRACT
When filing for personal bankruptcy, an individual can, in almost all cases, claim an
exemption for retirement assets. Using the Survey of Consumer Finances from 2007 and 2010,
we test the theory that highly educated or financially sophisticated households allocate more
resources to retirement assets under conditions of higher probability of filing for personal
bankruptcy. This hypothesis stems from the concept of asset sheltering, in which an individual
will demonstrate a preference for assets that are exempt from a particular risk.
To address our hypothesis, we run a Heckman model on the Survey of Consumer
Finances data. Our results provide evidence to match our theory for only highly educated or
financially sophisticated individuals, conditional on owning retirement assets. That is, we
observe highly educated and financially sophisticated households allocate more resources to
retirement accounts when they are at higher risk for bankruptcy. Other characteristic groups do
not demonstrate a similarly strong relationship between the probability of filing for bankruptcy
and the level of retirement assets.
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ACKNOWLEDGEMENTS
I would first like to thank my committee chair, Dr. Smith, for all the hard work put into
this project and the valuable guidance provided along the way. I am fortunate to have had the
opportunity to work in a supportive and uniquely insightful environment, in a dynamic,
fascinating field. This work, as well as much of my intellectual growth throughout the MS
program, would not have been possible without the exceptional mentorship and support.
I would also like to thank Dr. Geyer and Dr. Davis, as well as Dr. You, who were
constantly willing to guide and constructively advise my progress.
Many thanks go out to the rest of the graduate professors in the AAEC department,
especially those whose class I had the privilege of attending.
Finally, I’d like to thank Peter Caffarelli and Darren Enterline for the advice and support
and for helping to foster a supportive and intellectual environment among graduate students.
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TABLE OF CONTENTS
Chapter 1: Introduction ...................................................................................................1
Chapter 2: Background ....................................................................................................3
2.1 The Bankruptcy Process................................................................................. 3
2.2 Determinants of Bankruptcy Choice ..............................................................4
2.3 Retirement Assets.............................................................................................5
2.3.1 Background on Retirement Assets ..................................................5
2.3.2 Loss of Liquidity ...............................................................................7
2.3.3 Excess Contribution Penalty ............................................................7
2.3.4 Tax Deferment ...................................................................................8
2.3.5 Bankruptcy Exemption ..................................................................10
Chapter 3: Literature Review .........................................................................................12
3.1 Efficiency Losses from Bankruptcy Exemptions ........................................12
3.2 Participation in Tax Shelters ........................................................................13
3.3 Bankruptcy Exemptions as an Implicit Tax Shelter ...................................15
Chapter 4: Theoretical Framework ...............................................................................17
4.1 Utility Model ...................................................................................................17
4.2 The Decision between Retirement Plans and Liquid Savings Accounts ...20
4.3 Numerical Examples ......................................................................................22
4.3.1 Example 1 .........................................................................................22
4.3.2 Example 2 .........................................................................................22
4.4 Factors Related to Retirement Plan Contributions ....................................24
4.4.1 Income ...............................................................................................24
4.4.2 Education and Financial Sophistication ........................................26
4.4.3 Age .....................................................................................................27
4.4.4 Marginal Tax Rate ...........................................................................28
4.4.5 Liquidity and Savings Preferences .................................................29
4.4.6 Family................................................................................................30
Chapter 5: Data ................................................................................................................32
5.1 The Survey of Consumer Finances ................................................................32
5.1.1 Survey Design ...................................................................................32
5.1.2 Weighting and Implicates................................................................33
5.1.3 Creation of Pooled Data ..................................................................34
5.2 Variable Definitions ........................................................................................34
5.2.1 Independent Variables ....................................................................34
5.2.2 Interaction terms ..............................................................................38
5.2.3 Dependent variable ..........................................................................38
5.3 Descriptive Statistics .......................................................................................38
Chapter 6: Models............................................................................................................40
6.1 The Probability of Filing for Bankruptcy .....................................................40
6.2 Evidence of Sheltering ....................................................................................42
6.2.1 The Heckman Model........................................................................42
6.2.2 Marginal Effects ...............................................................................44
6.3 Model for the Expected Benefit of Retirement Asset Exemptions .............45
6.4 Model Specification and Variable Selection .................................................48
6.4.1 The Heckman Model Part 1 ............................................................49
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6.4.2 The Heckman Model Part 2 ............................................................50
6.5 Other Model considerations ...........................................................................51
6.5.1 Bootstrapping ...................................................................................51
6.5.2 Imputation Adjustments .................................................................52
Chapter 7: Results............................................................................................................53
7.1 Model Parameters ..........................................................................................53
7.1.1 Heckman Coefficients .....................................................................53
7.1.2 Marginal Effects ..............................................................................56
7.2 Expected Benefit Calculations .......................................................................59
7.2.1 Changes in PB .................................................................................59
7.2.2 Changes in Financial Sophistication and Education ...................61
7.3 Graphical Representation ..............................................................................62
Chapter 8: Conclusion .....................................................................................................65
8.1 Important Findings .........................................................................................65
8.1.1 Portfolio Reallocation ......................................................................66
8.1.2 Expected Benefits .............................................................................66
8.2 Limitations and Future Research ..................................................................67
8.3 Concluding Remarks ......................................................................................69
References .........................................................................................................................71
Appendix A: Expected Retirement Assets Graphs .......................................................73
Appendix B: Expected Relative Benefit Measures .......................................................77
Appendix C: Expected ....................................................................................................78
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LIST OF TABLES
TABLE 1: Descriptive Statistics for Total Population .................................................38
TABLE 2: Descriptive Statistics by Financial Sophistication and Education ...........39
TABLE 3: Descriptive Statistics for PB Variable .........................................................41
TABLE 4: Descriptive Statistics for Filers and Non-Filers in the 2009 SCF Panel ...41
TABLE 5: Heckman Model Results, Part 1 ..................................................................53
TABLE 6: Heckman Model Results, Part 2 ..................................................................54
TABLE 7: Unconditional Marginal Effects of PB by Subpopulation .........................56
TABLE 8: Probability Marginal Effects of PB by Subpopulation ..............................57
TABLE 9: Conditional Marginal Effects of PB by Subpopulation .............................58
TABLE 10: The Impact of Reallocation on Protected Assets ......................................59
TABLE 11: Changes in Expected Benefit due to Changes in Financial
Sophistication and Education .........................................................................................61
1
Chapter 1: Introduction
According to the United States Courts, the average number of non-business bankruptcy
filings in the US from 2000 to 2005 reached 1.57 million annually before seeing a sharp decline
to 598 thousand filings in 2006 after the passing of the Bankruptcy Abuse Prevention and
Consumer Protection Act (BAPCPA) of 2005. However, after 2006, the number spiked upward,
reaching a mid-recession high of 1.54 million in 2010, or 1.4 percent of all US households (US
Courts 2013). These high filing rates elevate the importance of bankruptcy in the United States
and its impact on consumers and suppliers of credit.
A large determinant of a household’s post-bankruptcy welfare, as well as its decision to
file, is the level and type of assets that he is allowed to own after filing. This situation is
governed by bankruptcy law with respect to exemptions, which designate those assets that cannot
be claimed by a creditor during bankruptcy. In particular, special legal attention has been given
to the exempt status of retirement assets, especially amid the uncertainty surrounding the recent
economic downturn. The BAPCPA extended exemption protection on the federal level to most
retirement accounts that were not previously covered. However, current research has left many
questions unanswered about the impact of such protections on investment behavior and the
impact of the policy on different population segments. This thesis attempts to answer those
questions by measuring the effect of exemptions for retirement assets on investment in
retirement accounts.
We begin the discussion with background information in Chapter 2 on bankruptcy in the
United States as well as the legal status of retirement accounts to provide context for the current
environment in which investment decisions are made. The literature review, Chapter 3, will
inform the discussion by shedding light on similar policy decisions and their disparate impacts
on certain population groups. Previous documentation of disaggregate responses to a similar tax
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policy will be important for identifying mechanisms by which individuals optimize their
portfolio choice.
This thesis will contribute to the literature by focusing on bankruptcy exemptions for
retirement assets and its impact on portfolio choice and welfare. Chapter 4, our theoretical
framework, will define our predictions regarding behavior, which we will test with data from the
Survey of Consumer Finances, described in Chapter 5. In Chapters 6 and 7, we construct a
model to measure behavior and welfare gains and report the results. Chapter 8 concludes with a
discussion of the results and their implications.
3
Chapter 2: Background
The following sections describe the process of filing for bankruptcy and some of the
primary factors that contribute to an individual decision to file. Next, we discuss the evolution of
retirement assets and the current tradeoffs faced by an individual considering contributions to a
retirement plan.
2.1 The Bankruptcy Process
The bankruptcy process is governed by Title 11 of the United States Code, adopted by the
Bankruptcy Reform Act of 1978 as a way to allow debtors an opportunity to regain financial
stability without being burdened by previous debt (Government Printing Office). An individual
who does not have the financial ability to repay creditors can use current bankruptcy protection
in the United States in various forms to discharge or reorganize debt in exchange for the
repayment of some debts to the extent of his ability to pay without being unduly burdened.
Thus, all United States citizens will have an effective partial insurance against unfortunate or
unpreventable financial events, such as medical debt.
In almost all cases, a bankruptcy case is filed by the individual debtor, rather than the
creditor, to initiate the process. The individual has several choices about which form of
bankruptcy he will pursue, usually Chapter 7 or Chapter 13. Chapter 7 allows greater protection
for the individual’s assets by extending protection to a specified list of exempt assets, and
otherwise discharging unsecured debt. However, Chapter 7 also requires that nonexempt assets
be surrendered to the courts for redistribution to creditors. On the other hand, Chapter 13 keeps
debts intact but initiates a court-supervised reorganization of financial assets. The Chapter 13
debtor is required to have current income to meet the repayment goals set by the debt
consolidation plan, unsecured debt, and must also have secured debt levels below specified
amounts. For 2013, that amount is $1,149,525. Other chapter choices, not examined by the
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present study, are available in infrequent circumstances; for example, farmers and fisherman are
eligible to file for Chapter 12.
The proceedings occur at the local level in a bankruptcy court, but bankruptcy rules are
governed by federal and state law. The trustee, who liquidates the debtor’s assets, sets aside
those assets that are ruled to be exempt. In some cases, state law allows specific exemptions for
a type of asset. In other instances, federal law universally mandates certain exemptions. Of
interest to the research here, the exemptions for retirement assets, are in the latter category. For
those assets that are covered by either type of bankruptcy exemptions, the debtor is allowed to
keep those assets. Any uncertainty surrounding an asset is judged by the bankruptcy courts.
In recent years, new legislation has incrementally increased the amount of exemptions
that can be claimed by a debtor in bankruptcy court as a means to allow ample opportunity for a
fresh financial start. One such asset type that underwent legislative evaluation for exemption
eligibility is retirement assets. Each type of retirement plan was evaluated separately and almost
all were granted exempt status. The legislative decisions surrounding exemptions for retirement
assets and the controversies surrounding the court’s judgment are discussed in Section 2.3 for
each type of retirement asset.
2.2 Determinants of Bankruptcy Choice
The decision to file for bankruptcy is not simple. Standard economic theory suggests that
people will file for bankruptcy when it is financially beneficial to do so. Filing after a negative
income shock will serve as an insurance mechanism for smoothing consumption (Blundell
2008). In these cases, bankruptcy law successfully protects consumers against events that are not
their fault, while expecting debt repayment to the extent that the debtor is able to pay (Grochulski
2010).
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Several behavioral factors complicate this ideal objective. In some cases, social factors
prevent individuals from filing, even amid financial hardship. A study by Fay, Hurst, and White
suggests that many people who do not file for bankruptcy would benefit from doing so. They
suggest that social stigma may play a significant role (Fay, Hurst, and White 1998). If social
stigma serves as an incentive to refrain from filing, then it may prevent debtors from taking
advantage of the benefits of filing. In other words, debtors treat social stigma as an additional
cost to filing for bankruptcy above the traditional financial costs.
Other incentive problems permeate bankruptcy decisions. For example, an individual
might decide to file because of a financial gain, regardless of his latent or overt ability to pay his
current debts. One study suggests that people have the ability to pay more than their bankruptcy
choice requires (Neubig, Jaggi, and Ernst 1999). Furthermore, research shows that the level of
exemptions that can be claimed by an individual in bankruptcy has an enormous effect on his
chapter choice (Domowitz 1993). The adverse effects of bankruptcy exemptions are discussed in
the literature review in the context of retirement plans. First, we present background information
on retirement assets and the legal environment surrounding retirement accounts.
2.3 Retirement Assets
2.3.1 Background on Retirement Assets
The decision to contribute to a retirement account is complex and multifaceted. An
individual’s cost-benefit analysis includes many desirable and undesirable outcomes, which must
be weighed against one another. We begin with a discussion of the benefits and drawbacks of
retirement accounts to explore the tradeoff faced by an individual, and continue in the
Theoretical Framework section, we present a model that explains the tradeoff between saving in
a taxable liquid account or contributing to a retirement account that would be exempt from
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creditors during bankruptcy. Finally, we will discuss individual characteristics that influence
retirement account contributions, as predicted by our cost-benefit analysis.
There are many types of retirement plans that are characterized by the investor’s ability to
choose his contribution levels. For the purposes of this research, we are interested in these plans
because of their discretionary feature. The ability to have control over contribution levels is an
essential component for our analysis of the impact of bankruptcy exemptions on personal
retirement planning choice. The two primary types of plans that comprise discretionary
retirement contributions are tax-deferred retirement plans (TDRPs) and Individual Retirement
Accounts (IRAs). Each of these types of retirement plans, as well as their respective subgroups,
have several characteristic differences. For example, a TDRP exists through one’s employer,
while IRAs are privately funded (with the exception of SEP IRAs and SIMPLE IRAs). These
differences are less important for our analytical framework than the similarities among
retirement plans, which are discussed below.
These retirement accounts were created and defined by the US Congress in the 1970s and
the 1980s to govern contributions to retirement plans from employee income. The explicit
purpose was to establish investment vehicles that would encourage greater levels of retirement
savings. Congress stated that it “was concerned that a large number of the country’s workers …
face the prospect of retiring without the resources needed to provide adequate retirement income
levels” (Congress 2003, 88). Thus, retirement contribution plans were created with special
treatment and features that would make them more attractive to individuals who are determining
their level of retirement savings. One example is that some retirement assets are not included in
calculations of assets for financial aid purposes for one’s household. The following
characteristics are relevant toward understanding our theoretical model.
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2.3.2 Loss of Liquidity
The purpose of retirement plans as an investment tool is to encourage savings that will be
later used for income after retirement. Because of this intended goal, retirement plans were
equipped with a mechanism by which funds would be partially committed to the account until
retirement: a withdrawal penalty. Any individual under the age of 59½ must pay a 10 percent
tax penalty on all withdrawals from an IRA or TDRP, with several exceptions for special
circumstances. The purpose of the penalty is to remove the temptation to withdraw funds prior
to retirement and to ensure that prior contributions will indeed be used for retirement purposes.
Using the account for any other purpose would be expensive to the individual.
However, individuals are not fully committed to using those funds for retirement
purposes. Although there is a significant tax penalty, an account holder can withdraw funds
early if doing so is worth the expense. This feature allows the individual to opt out of using the
retirement savings in the event of extreme or emergency situations. This is comparable to other
assets which are not fully liquid, such as Certificates of Deposit, for which penalties exist for
early withdrawal.
The choice between placing one’s assets in an IRA or TDRP and choosing some other
type of account weighs the cost of this commitment. When one chooses an IRA or TDRP, he is
losing liquidity, thus diminishing the ability to use those funds for outside loans, income
smoothing, emergency situations, or any unforeseen circumstance.
2.3.3 Excess Contribution Penalty
Another important feature of IRAs and TDRPs is the limit on annual contributions. For
IRAs, as of 2013, individuals can contribute no more than $5,500 for those under age 50, and
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$6,500 for those age 50 and over. For TDRPs, the limit is $17,500 for those under age 50 and
$23,000 for those age 50 and over. Other limits to employer contributions apply.
The exception to the contribution limit for IRAs is those with especially low income: one
cannot contribute more than 100% of his taxable compensation for the year. For IRAs, any
amount over this limit is taxed at an annual rate of 6 percent of the amount of excess, if it is not
withdrawn before the end of the year. For TDRPs, excess contributions are not allowed.
Furthermore, high-income individuals are not able to contribute to IRAs and TDRPs after certain
phase-out limits, which depend on filing status.
Placing a limit on the amount that one can contribute to a retirement plan leaves low-
income individuals generally unaffected, while high-income earners cannot take full advantage
of the benefits of an IRA or TDRP. This leaves retirement plan benefits to target those people
who have lowest incomes, intended to benefit the savings of those who need it most. Limiting
contributions to 100 percent of income ensures that individuals are truly intending contributions
for retirement planning.
However, similar to the withdrawal limit, the contribution limit can be bypassed after
paying a tax penalty for IRAs. This means that in certain situations, an individual might choose
to contribute a greater amount if the benefits of contribution more than offset this cost. Our
theoretical model treats the annual excess contribution limit as a cost for the IRA portion, but the
excess contribution limit is not binding in that case.
2.3.4 Tax Deferment
The negative features of retirement plans are balanced against those beneficial features
which were intended to encourage retirement savings. The most prominent feature is the ability
for an individual to reduce taxable income by contributing to tax-deferred retirement plans (with
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the exceptions for contributions to Roth accounts). For those tax-deductible plans, one’s taxable
income is lessened by any amount that he adds to his account in the same year. Furthermore,
interest, capital gains, and dividends on investments are tax-sheltered until withdrawal. Only
when an account holder makes a withdrawal from his account, he must then claim the amount of
withdrawal as income. Thus, taxes are not required to be paid on those assets until they are
withdrawn, which is usually after retirement. This benefit is diminished by the fact that gains are
taxed at withdrawal as well, where they are taxed as ordinary income and not at the lower capital
gains tax rate.
The tax deductibility and tax-sheltered status of retirement plans are intended to
encourage higher levels of retirement planning. The burden of paying current taxes weighs into
an individual’s decision to contribute. Additionally, those with higher marginal tax rates will
find this benefit to be especially helpful. First, upon withdrawal, they might have lower taxable
income during retirement years than they did mid-career. Also, for years that the account
experienced dividends or interest, an account holder might have high marginal tax rates as well.
In that case, deferring this income to post-retirement years will in many instances diminish the
rate at which those gains will be taxed.
The size of the benefit of the tax treatment of retirement plans depends on several factors.
Namely, the benefit depends on the relative value of one’s current marginal tax rate, one’s future
marginal tax rate during capital gains and interest, and the marginal tax rate post-retirement.
This feature is treated as a benefit in our theoretical model, measured by the values listed above,
and weighed against the opportunity costs of contributing.
2.3.5 Bankruptcy Exemption
10
The characteristic of retirement plans that is of greatest interest to this study is their
exempt status during personal bankruptcy. All assets in an IRA or a Roth IRA up to $1,000,000,
indexed for inflation from 2005, are exempt from the claims of creditors during bankruptcy
proceedings. A bankruptcy judge is allowed to increase this limit if he deems the credit Keoghs,
401(k)s, 403(b)s, and are all exempt with no limitation on the dollar amount. Prior to 2005,
individual state governments and courts made judgments about bankruptcy exemptions for IRA
and 403(b) plans. The exempt status of 403(b)s and IRAs was federally mandated in 2005 with
the BAPCPA. Prior to 2005, state legislature was allowed to decide policy for those assets.
Other retirement plans were mandated to be exempt by the Employee Retirement and Income
Security Act of 1974 (ERISA).
The purpose of this exemption for retirement assets was to insure those assets; that is, to
protect future income security from current income shocks. No matter how deeply in debt an
individual is, the option of filing for bankruptcy can help to keep his future savings intact. This
adds security to retirement plans, making them more attractive to investors, which is expected to
increase savings for retirement. It also serves to extend the insurance benefits of filing for
bankruptcy. Because of this goal, certain transfers from a nonexempt asset type to an exempt
asset type are considered fraudulent. If the debtor contributes a large amount to an exempt asset
type very close to the date of filing, the exchange is invalidated and the transferred assets are
considered to be nonexempt. This places a limitation on large, time-specific shifts in debtor
behavior in anticipation of bankruptcy, but does not explicitly limit less extreme transfers.
Individuals who file for Chapter 7 bankruptcy benefit from the exemption by the amount
in their exempt account. Measured by opportunity cost, the exempt status of retirement assets
saves bankrupt individuals the amount that they have previously contributed. On the other hand,
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those individuals who never file for bankruptcy receive no benefit from the exemption. The
exemption, then, leaves an uneven distribution of benefit across people.
We include the exemption as a benefit in our theoretical model as an expectation of
benefit. This benefit depends on whether the individual will ever file for bankruptcy. We
theorize that individuals have some information prior to bankruptcy about themselves by which
they evaluate the probability of eventually filing for bankruptcy. This information will lead to an
expected probability of whether they will be in the group of those that use the benefit (bankrupt
individuals) or of those who do not (individuals who never file for bankruptcy). In turn, this
expectation will determine the magnitude of the expected benefit of the exempt status of their
retirement assets. Similar to other beneficial properties of retirement plans, the exempt status
will be weighed against costs of contributing to the plan.
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Chapter 3: Literature Review
The current literature is extensive with respect to bankruptcy and the impact of
bankruptcy exemptions on microeconomic behavior. First, we discuss the justification for the
existence of bankruptcy exemptions and their insurance benefits to debtors. Counterbalancing
these benefits are several negative collateral consequences that have the potential to harm certain
types of households. Here, we document the effects that previous research has discovered, and
then examine bankruptcy exemptions through the lens of asset sheltering by drawing parallels
with other types of asset sheltering.
3.1 Efficiency Losses from Bankruptcy Exemptions
A great deal of the literature emphasizes and measures the positive moderating effect of
bankruptcy on negative income shocks. Some research indicates that bankruptcy exemptions can
be an alternative to other forms of wealth redistribution in public policy (Grant and Koeniger
2009). However, the collateral effect of bankruptcy exemptions extends across various types of
behaviors – primarily filing rates, credit supply, and interest rates.
One negative aspect of bankruptcy exemptions is the moral hazard problem. Individuals
may choose to undertake riskier behavior as a result of being protected by insurance. One study
by Grant (2010) exploits state-level exemption policy differences and examines the impact of
higher exemption levels on the amount of unsecured debt as well as life cycle consumption
patterns. Grant (2010) found that individuals with higher exemptions tended to prefer greater
unsecured debt, but also had smoother consumption levels across one’s life. Similarly, Athreya
(2006) found that higher levels of exemptions causes some individuals to be more likely to
declare bankruptcy in the first instance. This research demonstrates the tendency for individuals
to use bankruptcy laws as exemptions increase.
13
Athreya (2006) highlighted another negative consequence of bankruptcy exemptions –
credit availability. The insurance benefits of bankruptcy are mitigated by the loss in credit
availability to those that are at most risk for filing and discharging debt. According to the WEFA
Group (1998), creditors lose $40 billion annually from personal bankruptcy exemptions as a
result of their inability to collect certain assets against loans they have issued. Economic theory
predicts that creditors respond to decreased prospects of profitability for risky individuals by
charging higher interest rates and restricting credit availability. In other words, as the cost of
providing credit increases, supply diminishes, resulting in a higher price and lower quantity
supplied of credit. In agreement with standard economic supply and demand theory, the
Congressional Budget Office shows that demanders of credit (debtors) undertake some of the
costs of bankruptcy exemptions to creditors (Kowalewski 2000). However, in this case,
additional costs emerge from bankruptcy exemptions. The report points out that some of the
losses are borne by taxpayers as a result of the tax-deductibility of losses for businesses. That is,
if a debtor fails to pay a loan, the creditor can deduct the amount of the loss from the taxable
income of his business or his personal tax return. Furthermore, bankruptcy courts are subsidized
by the government, incurring further taxpayer losses (Kowalewski 2000).
3.2 Participation in Tax Shelters
For this study, we will examine investment in exempt assets to determine a disparate
effect of bankruptcy exemptions on different groups. The primary problem is participation in
investment in exempt assets. Participation has come under scrutiny in recent policy research
because of its importance in measuring the effectiveness of a particular law, especially tax law.
If a policy intends to benefit a specific subset of Americans, for example low-income
households, then participation by that group is crucial to ensuring the success of the policy. If,
14
on the other hand, there are financial or informational barriers to participation that impact the
targeted group disproportionately, then participation problems will be expected to undermine the
effectiveness of that policy for benefitting that group (Boylan and Frischmann 2006).
Examples of the participation problem abound throughout the literature across a wide
variety of policies. One such example examines the complexity surrounding financial aid forms
in higher education and whether such complexity impedes the intended benefactor, students from
low-income households. The study concludes that the distributional goals of the policy are offset
by the unnecessary complexity in financial aid rules because complexity disproportionately
harms low-income households (Babiarz and Yilmazer 2009).
Another study by Dynarski and Scott-Clayton (2006) demonstrates a mechanism by
which privileged households are able to benefit from such a policy. The answer lies in the fact
that those assets that are exempted from financial aid calculations hold greater financial benefit
to those intending to attend a college or university under financial aid. However, those with the
greatest ability to pay are more likely to recognize those benefits and favor those assets. The
result is that those who need aid the least possess the greatest share of those exempt assets and
can pull more financial aid away from those who need it more (Dynarski and Scott-Clayton
2006). This is in line with other research that demonstrates that financial sophistication impacts
the extent to which an individual uses the advantages of a particular tax policy. For example,
one study uses tax benefits for IRAs to demonstrate the positive impact of sophistication on the
receipt of tax benefits (Smith et. al, 2012).
The emphasis of current literature addressing policy effects upon those asset types that
are advantaged by tax rules demonstrate collateral effects that may be counterproductive to
redistributive or equity goals. The current body of research, however, leaves unanswered several
15
relevant considerations about retirement asset bankruptcy policy and whether exemptions are
received differently by various characteristic groups. Are some individuals more likely than
others to have portfolios that accurately price the expected financial benefit of bankruptcy
exemptions for certain assets? Who has a greater share of the exempt assets in the first instance?
3.3 Bankruptcy Exemptions as an Implicit Tax Shelter
Before we can answer these retirement asset bankruptcy policy questions with our
models, we must first examine the impact of exemptions on different groups.
One study by White (2006) found, in agreement with other literature (Grant 2010, Ellis
1998, Pavan 2008), that bankruptcy exemptions cause individuals to increase risky portfolio
allocation, file for bankruptcy more often, and work fewer hours after filing for bankruptcy. It
also examined redistributive effects across those who can take advantage of bankruptcy
exemptions and those who cannot. In conclusion, the study found that exemptions cause
redistribution of wealth from low-asset borrowers to high-asset borrowers and from states with
low exemptions to states with high exemptions (White 2006). This redistributive effect,
emerging from a problem of asymmetric participation, is a barrier to some individuals in
receiving intended benefits of greater exemption policies. Thus, participation and the receipt of
benefits will be a major focus of our econometric model.
Furthermore, research has shown that the availability of credit is not equivalently
impacted across demographics. A study by Gropp, Scholz, and White (1997) found that low-
asset households in high-exemption states had lower debt and higher interest rates for auto loans
than did households in low-exemption states. The authors find that exemptions redistribute
credit to households with many assets because they benefit to a greater extent from exemptions
(Gropp, Scholz, and White 1997).
16
Even more problematically, some have suggested that the riskier borrowing and lesser
credit leaves debtors hardly better off at all (Pavan 2008). If households with high levels of
certain assets are benefitting from exemptions, but the net welfare gains are negligible, it follows
that certain households may be worse off due to high levels of bankruptcy exemptions at the
expense of those with high asset levels. Our question of interest, then, narrows in on the
consequences of a neglected subset of bankruptcy exemptions: exemptions for retirement assets.
The above research demonstrates some of the negative aspects of bankruptcy protection
and exemptions. By comparison, other policies that help an individual avoid an implicit tax are
often affected by asymmetric participation, which helps certain demographics benefit from the
policy to a greater extent than others. Our research will complement the current body of work on
bankruptcy exemptions and participation in implicit tax shelters by investigating whether the
investment and savings of different types of households are affected disproportionately by the
exemptions for retirement assets. Specifically, we will test two things. First, whether financially
sophisticated or highly educated individuals are more likely to recognize and take advantage of
the expected benefits of the exemptions, and second, what characteristics are related to having
high levels of asset protection from the exemptions. Our theoretical framework examines these
savings decisions in more detail and theorizes how retirement asset exemptions can impact a
portfolio decision.
17
Chapter 4: Theoretical Framework
An individual will contribute to a retirement account if he expects that the marginal
benefits of contributing are greater than the marginal costs. Our theoretical framework builds off
this concept by weighing the key costs against the benefits of contributing. We assume that the
individual has already optimized his budget for investments and saving and has a certain after-
tax income available to save.
4.1 Utility Model
The costs of contributing to a retirement account are twofold: 1) the loss of liquidity and
excess contribution penalties, and 2) the opportunity cost of contributing to some other
investment. Thus, we can examine the net benefit of contributing to a retirement plan
(accounting for costs) and weigh them against contributing to some other liquid asset. These
benefits, expressed in terms of relative expected utility, must incorporate the investor’s risk
aversion into the distribution of returns. We begin with the following necessary condition for an
individual’s contribution to a retirement plan:
)) )) (1)
where the following representations apply:
) = the expected utility the wealth in one’s retirement account
the wealth in one’s liquid savings account
This relative utility measure represents the individual’s preferences for one portfolio
choice against another. This differs from an expected wealth model in that expected utility
incorporates risk preferences in addition to expected return. Many risk preference models could
accommodate this choice, but we will use the constant relative risk aversion model as an
example. The model was developed by Pratt (1964) and Arrow (1965) and states the following:
18
)
(2)
, W is wealth, and U is utility as a function of wealth.
Using this model, Equations 1 and 2 expand according to the relative values of the
retirement plan contributions and the liquid assets. The following representations apply:
expected probability of filing for bankruptcy
In order to define the expected benefit of contributing a dollar to a retirement plan, we
use the estimated probability of filing for bankruptcy. If the account holder does file for
bankruptcy, then the benefit to wealth is the exempted amount of his retirement plan balance. If
he does not, then those retirement assets are distributed to creditors. The probability of
bankruptcy serves as weights for the expected wealth.
Another important factor that contributes to a person’s decision to contribute to an
investment is the amount of risk that he is willing to accept. Because different investors have
variable preferences for risk acceptance, we use a coefficient, Z, to represent the distribution of
utility across quantity of risk. Although the model below cannot define Z, we can assume it is
constant within individuals but varying across individuals.
The result is the following formula for the expected utility of a retirement plan,
substituting into Equation 2:
)
(3)
This expectation is weighted according to the probability of filing for bankruptcy:
19
( )) ( ( )) ) ( (
)) (4)
( )) (
)
) ) (
)
)
(5)
For a liquid asset, we can define their value to the investor below. Note that we are only
interested in the portion of the account that would be at risk during bankruptcy (ie the extent of
his debt obligations).
( )
(6)
( ( )) ( ( )) ) ( (
)) (7)
( ( )) (
)
) ) (
)
)
(8)
Since we are examining only the portion of the account that would be at risk during
bankruptcy, the value of the liquid savings account during bankruptcy would be much lower.
This value depends on chapter choice within bankruptcy. The following representation applies:
the probability of filing for any type of bankruptcy
= the probability of filing for Chapter 7
= the probability of filing for Chapter 13
= the wealth in a liquid account if one files for Chapter 7
= the wealth in a liquid account if one files for Chapter 13
By definition,
(9)
Thus, Equation 8 expands to
( ( )) ( )
) (
)
)
) (
)
)
(10)
For Chapter 7, the entirety of the at-risk portion of one’s liquid savings account will be
distributed to creditors. Thus, reduces to 0. For Chapter 13, the value of the liquid
20
savings account is simply discounted by the obligation to creditors. We designate this
value some constant proportion and reduce the above equation:
( ( )) (
)
) ) (
)
)
(11)
Thus, an individual will contribute to a retirement plan if, by Equation 1,
[ (
)
) ) (
( )
)]
[ (
)
) ) (
)
)]
(12)
These values depend on the contribution limit for the account and the value of the annual
returns, the time periods until withdrawal, and the marginal tax rates.
4.2 The Decision between Retirement Plans and Liquid Savings Accounts
We establish the following definitions:
)
after-tax return in a taxable liquid savings account
)
)
The expected value of the retirement account is represented below, derived from
Equation 5. Note that probabilities of filing for bankruptcy no longer apply, since the expected
utility of wealth in a retirement account does not vary according to whether the individual files.
( )) (
[ ) ) ] ( ) ) ) ∑ ) ) )
)
(13)
The value of the at-risk portion of the liquid account is represented in terms of its returns,
derived from Equation 11.
21
( ( )) [ (
( ) ) ) )
)
) (( ) ) ) )
)]
(14)
Substituting into Equation 12, an individual will contribute to an IRA if the following
conditions are true:
( [ ) ) ] ( ) ) ) ∑ ) ) )
)
[ (( ) ) ) )
)
) (( ) ) ) )
)]
(15)
Our hypothesis can be demonstrated by deriving the change in the expected utilities as a
result of changes in the probability of filing for bankruptcy.
( ))
(16)
( ( ))
(
( ) ) ) )
) (
( ) ) ) )
) (17)
Thus, the probability of filing for bankruptcy increases, the left-hand side of our decision
rule, Equation 15, stays constant, while the right-hand side decreases. This will tilt the portfolio
decision in favor of retirement assets.
The following numerical examples serve to demonstrate the mechanics of this model.
The examples account for the various factors that influence an individual’s decision to contribute
to a retirement plan, based on the net benefit of both options. The examples are evaluated in
scenarios where retirement accounts are exempt from creditors in bankruptcy and in scenarios
where retirement accounts are not exempt. The differences between the scenarios illustrates the
impact of exemptions on the decision between portfolio options.
22
4.3 Numerical Examples
4.3.1 Example 1: High Probability of Filing for Bankruptcy
Assume the following for a household that is considering contributing to an IRA.
) )
)
)
Solution. Based on the mathematical tradeoff presented, the household should contribute to an
IRA versus maintaining liquidity in savings account based on the following calculation:
(([ ) ) ] [ ( ) ) ) ) )])
)
( ) ) ) )
) (
) ) ) )
)
The computation results in the following relative utility measure:
) )
This example demonstrates the relative benefit of contributing to a retirement asset
instead of a liquid asset, using the case of IRAs. When the percentage probability of filing for
bankruptcy is high at 30 percent, the individual sees a high relative benefit of contributing to an
IRA. In the next example, we change the exempt status of IRAs, and we can see the isolated
effect of bankruptcy exemptions on this portfolio decision.
23
4.3.2 Example 2: Low Probability of Filing for Bankruptcy
Assume the parameters from Section 4.3.1 except the estimated probability of filing for
bankruptcy being and in this example. The decision is made post-
BAPCPA where the individual will be eligible to claim IRA exemptions if he does file for
bankruptcy.
Solution:
(([ ) ) ] [ ( ) ) ) ) )])
)
( ) ) ) )
) (
) ) ) )
)
The computation results in the following relative utility measure:
) )
In this example, the individual should prefer investing in a liquid asset instead of
investing in an IRA. This contrasts from Example 1, where the optimal decision was to invest in
an IRA. This example demonstrates that portfolio choice can be a function of the probability of
filing for bankruptcy. We would expect individuals with higher probabilities of filing for
bankruptcy to be more inclined to invest in IRAs when they are exempt. That is, the marginal
impact of IRA exemptions given these parameters is to shift personal preferences in favor of
IRAs away from liquid assets.
Several parameters within the model can vary either in favor of one type of contributions
or another. For example, with a different risk variable Z, the outcome could have changed in any
of the above examples. A less risk-averse individual (with a lower Z coefficient) will more
highly favor the liquid asset. Other endogenous factors, such as current marginal tax rates, may
24
impact the level of contribution, but also external factors play a large role. Both types of
determinants are discussed below.
4.4 Factors Related to Retirement Plan Contributions
W expect retirement plan balances to be positively related to the probability of filing for
personal bankruptcy, among other variables. Our models will accommodate this theoretical
framework by including variables that measure the probability of filing for bankruptcy. Amid
these variables of interest, our model will include several control variables to explain as much
variation in retirement assets as possible.
The following sections outline which variables will be used in the econometric model and
the rationale for their inclusion.
4.4.1 Income
Maintaining a comfortable standard of living depends on the amount of investment that
an individual undertook prior to leaving the workforce for retirement. The reason designated
retirement plans were established by the US government has always been to encourage savings
that will later be used for consumption during retirement. The inherent commitment mechanism
through the withdrawal penalty is intended to ensure that the benefits of the plan are used for
retirement. Thus, the level of investment in one’s retirement plan is a partial indication of the
future level of consumption post-retirement.
Based on life-cycle theory, we expect that low-income individuals will be unlikely to
expect a sharp increase in standard of living after retirement, and that high-income individuals
will be unlikely to expect a sharp decrease in standard of living after retirement. The life cycle
theory was developed by Modigliani as a way to explain savings and consumption during various
years over a lifetime (Modigliani 1966). According to the theory, individuals have a strong
25
preference for smoother consumption, and take steps to diminish the variation in his own
consumption across time. The theory predicts that during relatively high-income periods, the
individual will save a greater portion of his income, and in relatively low-income periods, the
individual will consume more than his income. During those low-income years, the individual
can facilitate higher consumption by two means: borrowing against future income, or
withdrawing from savings from previous periods. During retirement, where income drops off, in
an effort to smooth consumption, the individual consumes saving from previous periods.
According to the life cycle theory, variations in income across time can partially predict
which years an individual will prefer to save for future, post-retirement years. That is, high
income in a given year might predict savings whether the individual is typically a high-income
earner or not. Furthermore, it also predicts that individuals who typically have high income will
prefer to consume high levels during retirement, to smooth consumption against high pre-
retirement consumption. Thus, an application of the life cycle theory demonstrates that we
should expect a positive relationship between income and saving for retirement. Additionally,
high incomes are related to higher levels of liquidity, which will help the individual to contribute
to savings at his discretion. Low-income households tend to spend a higher percentage of
income on necessities and have less available to save (Gutter et al. 2012). We expect that these
households also have lower access to credit and less wealth from which to draw.
We also hypothesize that the loss in liquidity associated with contributions, which is
usually a significant cost of contributing, affects the finances of high-income individuals less
than low-income individuals. High-income individuals are better able to absorb negative income
shocks that might require liquidity. This means that high-income individuals are less affected by
one of the costs of contributing to a retirement plan.
26
To a greater extent, high-income individuals can take advantage of one of the benefits of
contributing to a retirement plan: tax deferment. High income is taxed at a higher marginal tax
rate than low income. Therefore, the benefit of deferring taxes to retirement might be greater for
high-income individuals, as he can avoid paying a high marginal tax rate that he might not
experience post-retirement when he withdraws. This is consistent with current literature, which
indicates that income is indeed a determinant of retirement plan contribution rates (Huberman,
Iyengar, and Jiang 2007).
4.4.2 Education and Financial Sophistication
When ERISA established new retirement plans, Congress expressed concern that
individuals were not investing enough in retirement assets and that many individuals would not
have enough funds to finance a comfortable level of consumption throughout retirement
(Congress 2003, 88). The express intent of retirement plans was to encourage individuals to
invest more so that the nation could avoid a problem at retirement of not having enough in
savings. Research and polling on individuals retirement planning lends support to the idea that
individuals are choosing a level of saving that is not based on optimal information. That is,
informational costs are greater than 0. For example, a recent poll showed that 56 percent of
households have not tried to calculate how much money they will need in retirement to live
comfortably (Helman, Copeland, and VanDerhei 2012). Although the barriers to making
optimal financial decisions are complex and not fully identified, it is apparent that understanding
finance is crucial to correctly estimating the benefits of a particular choice and to making
decisions in the long-term interests of the individual (Van Rooij, Lusardi, and Alessie 2012).
Understanding the complexities of finance and the laws it entails comes at a separate
cost. For example, knowledge about IRAs would drastically affect the examples given based on
27
our theoretical model. If an individual is unaware of the status of bankruptcy exemptions for
IRAs, then he will underestimate the benefit of contributing to his IRA. Although the IRA may
have a higher expected utility, the individual may choose to invest in a liquid asset instead,
without realizing the risk he is taking. In other words, while our model is valid, there is an
additional cost that is not modeled to represent the costs of implicitly computing the model in the
first instance.
As outlined in the literature review, individuals face varied barriers, or informational
costs, to optimally allocating financial resources. For some individuals, access to financial
literacy or wherewithal to develop a dependable expertise is not uniformly distributed. For those
with higher financial education, knowing and understanding the interplay of all financial
instruments and laws can highlight the benefits of a portfolio choice (Lusardi, Mitchell, and
Curto 2010). Modeling this problem as variable informational costs helps explain the
disproportionate impact of tax policies on different demographic groups.
To proxy for the benefits of education in reducing informational costs, we will use level
of education as a dependent variable in our econometric model. We expect that those with
higher education will more accurately estimate the benefits of retirement plans in the long term.
Therefore, total retirement assets are expected to be positively related to education levels.
Another measure, financial sophistication, which is explained in detail in the Data section, will
be included as well to determine its effect on retirement planning.
4.4.3 Age
As an individual ages, retirement nears his current time horizon. The closer to retirement
one approaches, the more apparent it becomes the precise level of wealth needed post-retirement,
as one gains new information on current salary, health and expected work years, and about how
28
much will be needed to consume after retirement to stay comfortable. Some individuals have
limits to the amount of time in advance that they will plan for their future. That is, in the present,
one is more likely to choose to disregard the needs of one’s future self if the time horizon is
distant. For this type of person, age will play a significant role in motivating retirement
planning. As one ages, the prospect of retirement comes into view, and one is more likely to
realize the urgency of proper planning.
The tendency to focus on the present is documented in literature and in the present bias
theory or time inconsistency (Laibson 1997). The theory states that an individual’s decisions are
made in such a way that they are at odds with future decisions. By focusing on one’s present
self, the decision maker can have devastating consequences to his own future self. This is often
viewed as a behavioral bias which justifies the existence of tax-advantaged retirement plans.
For those with this particular behavioral tendency, age will be a determinant of retirement
assets. This effect is combined with increased and improved information about one’s own
retirement and current income over time, which can motivate contributions as well. Finally, for
those age 50 and above, the contribution limit increases in all types of qualified plans. We view
this as a decrease in the cost of contributing additional funds after age 50, making retirement
assets more attractive relative to other investments. Thus, our model expects age pre-retirement
to be positively related to retirement assets, consistent with literature on retirement contributions
(Hira, Rock, and Loibl 2009).
4.4.4 Marginal Tax Rate
As mentioned in above in the discussion of income, individuals with high marginal tax
rates (MTRs) have an extra incentive to contribute. Because retirement plans are a tax-deferred
vehicle, the benefits of contributing depend on the current MTR that one is forgoing. If this
29
MTR is high, then deducting contributions saves the individual from paying a high MTR on the
amount of his contribution. Furthermore, earnings and growth in the account are tax-sheltered
until withdrawn. If the assets in an retirement account were instead originally placed in a more
liquid account, the earnings would be taxed at the MTR each year. In a retirement account, those
earnings avoid this high marginal tax up front and generates the possibility of overall tax savings
if an individual's tax rate is lower in the future at withdrawal.
Avoiding this tax is an extra incentive or reduction in cost of contributing to a retirement
plan. We can assume that an individual will respond to this incentive by investing more heavily
in a retirement plan if his MTR is higher. One can see this in the theoretical model: the
variable reduces the after-tax amount that may be contributed to a taxable liquid savings
account and therefore is directly related to being more likely to benefit from a tax-deferred
retirement plan. Thus, the impact of higher marginal tax rates on total retirement assets should
be positive (Long 1990).
4.4.5 Liquidity and Savings Preferences
The section on income explained that high-income individuals might be better able to
handle one of the costs of contributing to a retirement plan, the loss of liquidity. Having one’s
assets committed to an account with a steep withdrawal penalty might impose a bigger burden on
those who do not have a high level of wealth or income. However, income is not the only factor
that determines preferences for liquidity. Other factors, such as risk aversion, discount rate, or
characteristics of one’s overall portfolio might determine one’s optimal level of liquidity.
Liquidity preferences, in turn, will influence the relative value of a retirement account. If an
individual prefers high levels of liquidity, then the lost liquidity from contributing is an
additional cost that is weighed in the decision to contribute (Long 1990).
30
Similarly, the life cycle theory is not the only determinant of savings preferences. As
discussed in the overview of time inconsistency theory, individuals may have a stronger
preference for savings if they are more future-oriented. Other factors that may contribute to
savings preferences include investment options, educational costs, or income shocks. If an
individual has stronger preferences for saving for future consumption, regardless of the reason,
then we would expect higher retirement account balances. Since retirement plans are a form of
savings, total retirement assets should be related to overall preferences for saving.
Stronger preferences for liquidity and for savings are expected to be negatively and
positively related to retirement account assets, respectively. These exogenously-determined
variables should partially explain retirement account balances in our econometric model. As
such, it is necessary to control for these variables.
4.4.6 Family
The size and timing of a family greatly affects the level of income and consumption of
the household. It is expected that families with greater number of children will have greater
demands on their income to support current consumption for a larger number of household
residents. This places additional constraints on liquidity and ability to save, resulting in an
expected negative effect on retirement assets.
Furthermore, some evidence exists that children serve as an implicit partial insurance
mechanism for their parent’s future consumption and income (Pörtner 2001). This insurance
effect will, for some individuals, partially alleviate some of the need to save for future income.
We expect, then, that having children could negatively impact retirement savings for this reason
as well. Combined with the additional demand on current income, the overall marginal effect of
31
having children should be negative on retirement assets, consistent with Yang and DeVaney
(2012)
Having a spouse, on the other hand, may not have a negative effect on retirement
planning. Although additional household members will place additional demands on income, a
spouse may increase the household’s ability to contribute to a retirement plan. In spite of the fact
that a spouse may serve as future income insurance, we theorize that a spouse may increase
ability to pay or decrease informational costs. Furthermore, there are economies of scale
associated with a marginal household member. A married couple will have less than twice the
expected expenses of living separately.
Additionally, having a spouse increases the need for retirement plans in the future. If the
head of household expects to operate as one economic unit with his future spouse after
retirement, then the household’s retirement assets will need to be high enough to support both
individuals. Thus, there is a greater current need to build a high retirement account balance.
Thus, we expect that overall, the impact of a spouse to be positive on the chosen level of
retirement balances. Note that the effect of increased income has already been captured and
controlled for by the income variable.
32
Chapter 5: Data
5.1 The Survey of Consumer Finances
The data for our models draws from the Survey of Consumer Finances (SCF). The SCF
is a triennial study conducted by the Federal Reserve Board of thousands of households to
provide a comprehensive view of American finances. The household-level data covers a broad
range of topics including demographics, liabilities, debt, retirement assets, and income.
5.1.1 Survey Design
For our analysis, the 2007 and 2010 versions of the survey are included, along with a
panel from 2009 which resampled those households which were surveyed in 2007. The 2007
survey sampled 4,418 individuals, and the panel in 2009 was able to resurvey 3,857 of those
individuals. The 2010 survey increased the number of households to 6,482. For the analyses
here, the 2007 and 2010 surveys are combined into a pool of 10,900 households. These two
survey years give a detailed description of American finances after the BAPCPA came into
effect. These two surveys are the only two full surveys that occurred when all individuals are
certain to have bankruptcy protection for retirement assets post-BAPCPA.
Each variable included in the SCF is numerically coded based on survey responses. The
responses are all in number form, and sometimes represent dollar values. In other cases, specific
numbers correspond to a yes or no response, an item on a provided list, or a reference to a
specific household person. This coding method necessitates reclassification of all variables into
a form that can be analyzed or regressed.
In some cases, the variables used in the model were derivatives of a collection of survey
variables, discussed later. In addition to the financial variables, the SCF also includes attitudinal
and demographic variables which are useful as control variables in a regression model. The
33
variables in the survey used for the empirical analysis are described below, as well as a
description of the creation of new variables.
5.1.2 Weighting and Implicates
In an effort to convey the most information about US finances, the SCF intentionally
over-samples wealthy and high-income households, resulting in a non-representative sample.
We describe in brief the methods that are detailed by the FRB (Kennickell 1998). For
descriptive statistics or t-tests, the SCF includes a variable for the weight of each household
according how many households (out of the total 116 million) that are represented by this
observation. Those households with higher incomes or assets are given lower weights, since
they are relatively atypical among American households. Where descriptive statistics and t-tests
are used, the variables are properly weighted first.
The SCF also attempts to correct for another problem with its data: missing values. As
outlined by Kennickell (1998), the Federal Reserve Board uses multivariate analysis to predict an
expected value for the data here missing data exists in the survey results. In order to accomplish
this, each household is imputed, or replicated, five times, resulting in five separate implicates for
each variable per household. These five implicates provide a better estimate than just one
because multiple values can more accurately capture the likely range of values that are expected
from that respondent. This method provides the best possible estimate for the household’s
missing value given other known characteristics.
When using regression analysis, such imputations can bias the standard error of the
results, and necessary adjustments must be made to correct for this tendency. An article
published by the Ohio State University explains the procedure for correcting regression results
34
(Montalto and Sung 1996). These adjustments to standard errors are made in any regression
analysis in our empirical analysis, discussed in Chapter 6.
5.1.3 Creation of Pooled Data
For these models, the 2010 survey and the 2007 survey were pooled into a total sample
with 10,900 households and 54500 total imputations. Dollar values reported in the 2010 survey
were deflated to 2007 dollars according to the Consumer Price Index. The 2009 survey, which
uses the same individuals from the 2007 survey, excluded many typical variables included in
other survey years in order to make the panel more practical and manageable. Because of this,
there was not enough information to appropriately estimate the probability of filing for
bankruptcy. Later on, the panel is used here to test the validity of our probability estimate by
determining who the profile of those who did file for bankruptcy between the 2007 and 2009
surveys.
5.2 Variable Definitions
The variables used in the models range across demographic, attitudinal, and financial
variables, all derived from the Survey of Consumer Finances. All these variables were
reclassified to logically apply to a statistical modeling framework instead of reflecting survey
codes. In some cases, new variables needed to be created from a combination of other measures.
These processes are explained below.
5.2.1 Independent Variables
The first model, which will estimate each household’s probability of filing for bankruptcy
(PB), is explained in the Model section. The variables that contributed our first model were
primarily financial in nature. The main contributor to bankruptcy, debt, takes several forms that
have distinct relationships with bankruptcy. Because of these distinguishing characteristics, it
35
was necessary to specify the amount of debt held by each household in several categories based
on ownership of the loan, type of loan, and whether the loan was secured (collateralized with
property). The six categories of debt that were created were 1) credit card debt, 2) unsecured
debt owed to a bank or financial institution (other than credit card debt), 3) all other unsecured
debt, 4) secured debt owed to a bank or financial institution, and 5) all other secured debt and 6)
medical debt. The justification for these categories is discussed in the Model section.
To classify debt as secured or unsecured, we first observed the type of debt. Some types
of debt, such as credit card debt, is assumed to be unsecured, while others, such as house loans,
are assumed to be secured, unless otherwise specified. In those cases where the type of debt
does not imply secured or unsecured status, such as business loans, the SCF asks whether the
loan is secured by property. If the loan in either a type of loan that is typically unsecured, or
specified to be unsecured by the survey respondent, then we classified that debt as unsecured.
For most loans, this question preceded a question about to whom this loan was owed. In a
minority of instances, this question was not included. We assumed those loans were “other,” that
is, not owed to a bank or financial institution. Medical debt, which overlapped with other
categories of debt, is defined as any debt that is owed to a doctor, hospital, dentist, or
veterinarian.
Other variables contribute to the estimation of the probability of filing for bankruptcy,
some of which are used in our other models as well. The variable for married is a dummy
variable that includes both those individuals who are legally married as well as those who are
unmarried but living with a partner or spouse. House ownership is a dummy variable as well that
includes ownership of all types of houses – ranches, farms, mobile homes, houses, condos, etc.
36
The variable for debt includes all types of debt, and the variable for assets includes all types of
assets.
The variable for income was used in the estimation of the probability of filing for
bankruptcy in a unique way. Because the specification of the model used income to normalize
debt variables, those with incomes of 0 led to computationally impossible values for normalized
debt categories. In order to treat those individuals with no income as having low incomes and
high normalized debt values, we censored the income data from below at $500. For our other
models, the income variable simply measures the dollar values of income, bound from below by
0.
In explaining retirement assets, we use a wide array of variable types. First, we compute
the age of the head of household, and his or her age squared, as well as natural log of household
income. We also constructed dummy variables for whether the household has 0 children, 1
child, 2 children, or more than 2 children, as well as whether the household head has a bachelor’s
degree, to proxy for education. Another variable from the SCF for being married was
constructed by including households with either a couple that is legally married or domestic
partners. Race variables were also included to capture demographic variation – a dummy
variable for whether the individual is white and a dummy variable for whether the individual is
black. If the individual is neither black nor white, then both dummy variables will be 0.
Another dummy variable captures whether the individual is currently constrained for
liquidity. The household was classified as constrained for liquidity if he met two conditions: 1)
they were turned down for credit in the previous five years, and 2) they either were unable to
obtain credit by reapplying or decided not to reapply because they believed they would be turned
37
down. This variable proxies for the household’s opportunity cost for liquidity loss as a result of
holding assets in savings.
Some of our variables related to retirement plans directly. We constructed a variable for
whether the household head has access to a retirement plan through his employer in which both
parties can participate. Another variable measures whether the individual plans to retire in the
next five years. Aside from age, we expect that an individual will plan his retirement assets
based on how soon he will need them. Furthermore, to control for the expected returns on an
individual’s retirement assets, we calculate the percent of an individual’s retirement assets that
consist of “risky” assets with a high expected return, such as stocks.
To create a measure of financial sophistication, we duplicate previous measures from
Huston, Finke, and Smith. First, four factors are selected from the SCF: 1) an attitudinal variable
about the level of risk the individual is willing to take, 2) whether the individual currently
utilizes greater than 50 percent of his credit availability, 3) whether the individual owns stock
equity, and 4) a rank from 1 to 4 for the level of understanding of the SCF questions. The latter
variable is reported by the person who conducts the survey based how well the respondent
showed an understanding of the complex financial questions in the survey. Next, the four factors
are combined via factor analysis using the standard deviation from the mean for each factor.
Those who are more risk averse, are not utilizing high amounts of credit, own stock equity, and
have greater understanding of the survey are ranked higher. Finally, the individuals are split into
quintiles, where 1 represents the (weighted) 20% of individuals who ranked highest in the factor
analysis, and where 5 represents lower levels of financial sophistication (Huston, Finke, and
Smith 2007).
5.2.2 Interaction terms
38
We also created interaction terms to be used in the model. The first interaction variables
measured the impact of the probability of filing for bankruptcy and financial sophistication
jointly. The estimated probability of filing for bankruptcy was multiplied by each of the five
dummy variables for financial sophistication, one for each quintile. The other interaction
variable measured the impact of the probability of filing for bankruptcy and education jointly. It
was created by multiplying the estimated probability of filing for bankruptcy by the dummy
variable for whether the individual has completed a bachelor’s degree.
5.2.3 Dependent variable
Finally, we used a variable for the level of retirement assets owned by the household.
This variable uses the log total dollar amount of quasi-liquid retirement accounts, including
pensions, IRAs, and Keoghs. That is, it measures the percentage of a household’s total assets
that have been invested in a designated retirement account with a withdraw penalty.
5.3 Descriptive Statistics
The following descriptive statistics give us a clearer picture of the mean and the
dispersion of the data. All data from 2007 and 2010 are pooled.
TABLE 1: Descriptive Statistics for Total Population
Variable Frequency (Percent) Mean (Std Dev)
Income (000s) 79.51 (142.01)
Quasi-Liquid Retirement Assets (000s) 84.38 (139.95)
Age 50.32 (7.68)
Access to Employee Retirement Plan 31.66
Plans to Retire within 5 Years 4.17
Bachelor’s Degree 36.46
No Kids 56.30
1 Kid 18.29
2 Kids 15.59
39
3 or More Kids 9.81
Married 58.38
Black 13.32
White 72.06
Liquidity Constrained 27.22
By comparison, we include here a descriptive statistics table for the five quintile
classifications of financial sophistication and for the two levels of education. These descriptive
data demonstrate the characteristic difference of individuals with different levels of financial
sophistication and education. Each value represents the mean for the disaggregated groups, with
Quintile 5 representing those with lowest levels of financial sophistication, and Quintile 1
representing those with highest levels of financial sophistication. Dummy variables represent
percentages within the quintile with the relevant characteristic.
TABLE 2: Descriptive Statistics by Financial Sophistication and Education
Financial Sophistication Education
Variable Quintile 5 Quintile 4 Quintile 3 Quintile 2 Quintile 1
No Bachelor’s
Degree
Bachelor’s
Degree
Income (000s) 27.42 38.54 61.64 99.38 169.98 49.15 132.42
Quasi-Liquid
Retirement
Assets (000s) 1.45 6.74 35.57 120.56 256.43 30.30 178.63
Probability of
Filing for
Bankruptcy 4.33 4.97 7.25 6.44 4.17 7.82 4.04
Bachelor's
Degree 11.41 20.55 31.86 49.92 68.48 0.00 1.00
Married 41.84 50.64 59.94 63.83 75.57 0.56 0.57
No Kids 54.16 58.73 56.11 56.51 55.98 0.19 0.17
1 Kid 18.21 17.83 19.08 18.14 18.21 0.15 0.17
2 Kids 15.53 13.09 14.66 16.70 17.99 0.11 0.08
3 or More Kids 12.11 10.35 10.15 8.66 7.81 0.56 0.63
Black 22.76 17.03 14.29 8.87 3.69 0.15 0.10
White 54.45 66.37 70.17 81.09 88.19 0.69 0.78
40
Chapter 6: Models
6.1 The Probability of Filing for Bankruptcy
In order to determine the effect of bankruptcy on portfolio choice, we must first estimate
the probability of filing for bankruptcy for each household in the SCF. The probability of filing
for bankruptcy, while not observable, can be estimated via its relationship with other variables,
especially debt variables. Domowitz and Sartain used multiple nested logit models from the SCF
and interviews with bankrupt individuals to create a model that specified the magnitude of these
relationships (Domowitz and Sartain 1999). Using this model, we can quantify each explanatory
variable for households in the SCF and compute the probability of either Chapter 7 or Chapter 13
bankruptcy. Their model is defined as:
) )
) ) )
) )
) )
(18)
The variable “PB” is the probability of filing for bankruptcy. “Medical” is the amount of
medical debt divided by assets. “Homeowner” is a dummy variable for whether the individual
owns their home. “Married” is a dummy variable for whether the household consists of a
married couple or a couple living together. “Debt” is the debt-asset ratio in the household.
“Credit Card” is the amount of credit card debt divided by total assets. “Unsecured Bank” is the
amount of unsecured debt owed to a bank or financial institution, divided by total assets.
“Unsecured Other” is the amount of unsecured debt, divided by total assets, that is not on a credit
card and not owed to a bank or financial institution. As described in Chapter 5, the coefficient
on “Unsecured Other” has been averaged across two of Domowitz’s variables, the variables for
41
unsecured other debt and for unsecured individual debt. “Secured Bank” is the amount of
secured debt that is owed to a bank or financial institution. “Secured Other” is the amount of
secured debt, divided by total assets, that is not owed to a bank or financial institution.
The methods for creating and computing these variables are defined in detail in the Data
chapter. Our variable of interest is the PB variable, the probability of filing for bankruptcy,
bound from 0 to 100 percent. This variable will be used in the other models below.
The following table gives some information about the mean and dispersion of the
probability of filing for bankruptcy variable created in this model. There is a distinct difference
between the profiles in 2007 and 2010, with 2010 demonstrating a higher probability of filing on
average amid the economic downturn.
TABLE 3: Descriptive Statistics for PB Variable
Year Mean Probability (%) 25th Percentile Probability (%) 75th Percentile Probability (%) 2007 4.275 0 0.033 2010 6.205 0 1.502 Aggregate 5.423 0 0.831
To lend validity to the measure of PB as a predictor of bankruptcy, we demonstrate the
following descriptive statistics from the 2007 SCF, disaggregated by those who reported filing
for bankruptcy in the 2009 panel survey. This will allow us to follow a panel of individuals to
determine the characteristics of those who actually did file in time period t based on their
probability of filing in time period t – 1. The 2009 survey resampled the individuals from the
2007 survey with an 89% re-response rate. Using only those individuals resampled in 2009, the
table below disaggregates the PB variable by those who did report filing for bankruptcy between
surveys and those who did not.
42
TABLE 4: Descriptive Statistics for Filers and Non-Filers in the 2009 SCF Panel
2009 Panel Frequency (% of Total) Mean Probability (%)
Filed between 2007 and 2009 1.57 9.71
Did not file between 2007 and 2009 98.43 4.33
6.2 Evidence of Sheltering
In order to determine whether individuals with a higher probability of filing for
bankruptcy favor retirement assets, which are protected against bankruptcy, we first seek to
determine the effect of an increase in the probability of bankruptcy on the level of retirement
assets by different groups.
6.2.1 The Heckman Model
Hypothesizing that the selection of whether someone has greater than $0 in retirement
assets differs from the determinants of the level of retirement assets, we will use a Heckman
model to estimate the marginal effect of our PB variable at different levels of financial
sophistication (Heckman 1979). We first begin with a description of the Heckman model, and
establish the following:
if and if (19)
D indicates whether the person has any retirement assets, and Y represents the level of
retirement assets in dollars. We then continue with the first of two parts of the Heckman model.
In the first part,
| ) ) (20)
| ) ) (21)
43
Z is a vector of all our explanatory variables, γ is a vector of unknown coefficients solved
by the first part, and Φ is the cumulative distribution function of the standard normal distribution,
and is the density function.
The second stage is a least squares regression on the sample, censored to those
individuals where D = 1. However, the distribution of Y is bound on the left-hand side to 0. The
Heckman model treats our variable Y as if there is an underlying distribution not bound by 0.
This distribution cannot be fully specified in the same way that an OLS can be, and requires that
we include the Inverse Mills Ratio (IMR) to correct for this omitted variable problem.
We then compute the IMR as
)
)
)
(22)
This allows us to construct the second part of the model, where we specify the
conditional expectation of retirement assets on our censored sample, given a positive value for
our retirement assets variable. To measure retirement assets, we use the natural log of total
dollars in the household’s quasi-liquid retirement accounts, lnY. Our model is described as
follows:
| ) ) (23)
X is a vector of our explanatory variables, is an unknown parameter establishing a
relationship between the two steps of the model, and we solve for the vector of coefficients .
The X vector contains many of the same variables as the Z vector, which are both discussed in
Section 6.4.
The unconditional expectation of the entire sample, however, differs because the
unconditional expectation depends on both the probability that D = 1 and the expectation of Y
given that D = 1. Thus, our unconditional expectation of Y is the following:
44
| ) ) | ) (24)
| ) )( )) (25)
6.2.2 Marginal Effects
This model allows us to derive our value of interest, the marginal effect of an explanatory
variable on the level of retirement assets. The explanatory variable can impact one’s retirement
assets in two ways: 1) by changing the probability that an individual holds retirement assets, and
2) by increasing the expected value of an individual’s retirement assets provided that his asset
level is greater than 0. We refer to the first effect as the probability marginal effect and the latter
as the conditional marginal effect. The combined result of these two effects are called the
unconditional marginal effect.
The probability marginal effects are defined as
))
(26)
where is one explanatory variable. The conditional marginal effect is defined as
| )
(27)
Typically, the equation above reduces to (
), where is the coefficient on our
variable in the second stage of the Heckman procedure. However, for our interaction terms,
the derivation is more complex. For this example, we use and , where is the discrete
interaction variable. In our case, is either financial sophistication or education and PB is .
We will be primarily interested in the marginal effect of evaluated at each level of the discrete
variable .
45
| ) ∑
) (28)
| )
|
(
)|
(29)
This equation is instrumental for calculating our value of interest, the unconditional
marginal effects of PB evaluated at various levels of . The general case is defined as
| )
( ) | ))
(30)
(( )) (
| )
)) (( | )) (
))
))
For interaction effects, we will compute
)
|
(31)
This value will give us a picture of how the portfolio allocation of different population
groups changes with the probability of filing for bankruptcy increases.
6.3 Model for the Expected Benefit of Retirement Asset Exemptions
Portfolio reallocation in response to a policy reveals how an individual may alter his
behavior to benefit from the policy. These behavioral effects impact the distribution of benefits
of some policy. Here, we are interested in how portfolio sheltering impacts the distribution of
financial gain derived from bankruptcy exemptions for retirement assets.
The distribution of benefits from bankruptcy exemptions is important not only for its
policy implications, but also to provide a relative measure of the sheltering effect. Thus, we are
46
interested in calculating the distribution of these benefits themselves, and compute how much of
those benefits are due to asset reallocation.
To measure the benefit of retirement asset exemptions, we consider the two conditions
that are necessary for benefitting from the exemption: 1) filing for bankruptcy, and 2) possessing
retirement assets that are covered by the exemption. If either of these conditions are not met,
then no benefits of the exemption are realized. The level of benefit, if both conditions are met,
depends on two factors: 1) the chapter choice in bankruptcy, Chapter 7 or Chapter 13, and 2) the
level of retirement assets. If an individual files for Chapter 13 bankruptcy, retirement assets are
excluded from the calculation of total assets, which determines the repayment plan. The
bankruptcy exclusion therefore benefits Chapter 13 filers to the extent that it relieves repayment
obligations. If, instead an individual files for Chapter 7 bankruptcy, his retirement assets are
protected from creditors and he is relieved of those debt obligations.
Since our measure of the probability of filing for bankruptcy does not distinguish
between chapter choice, we assume that the expected dollar benefit of a marginal dollar in one’s
retirement plan is the average benefit of filing for each chapter, conditional on filing, and
weighted by the relative frequency of each chapter choice. The following representation applies,
where represents the percent probability of filing for any type of bankruptcy, is the
percent probability of filing for Chapter 7, is the percent probability of filing for Chapter
13, ) is the total expected financial benefit of the bankruptcy exemption for retirement
assets, ) is the expected financial benefits of the exemption conditional on filing for
Chapter 7 bankruptcy, ) is the expected benefit of the exemption conditional on filing for
Chapter 13 bankruptcy, and Y is retirement assets:
(32)
47
) )) )) (33)
We scale PB, which is measured in percentage terms, by .01. With a few exceptions for
exemption limits, we expect ) should be equal to the total amount of retirement assets, Y.
The expected benefit of the exemption for Chapter 13 filers is the amount by which exempt
assets relieves debt obligations relative to nonexempt assets. We expect this value to be some
constant factor of the total amount of exempt assets in one’s retirement account. We designate
this total value (where ) to reduce ):
) (34)
We assume minimal fluctuation in the relative probability of Chapter 13 versus Chapter 7
choice conditional on filing for bankruptcy. That is, we assume
and
are constant,
designated and respectively.
) ) (35)
) (36)
where , and is some constant, then we can we can reduce Equation 35 to a
form that is useful for specifying in our final model.
)
(37)
Our value of interest is the impact of retirement asset bankruptcy exemptions on some
characteristic or variable. Hypothesizing a log-linear relationship, we are interested in the
change in the percent E(B) as a result of some variable. That is, we will solve for ))
for
some variable from our previous model. This value is a function of Y and PB.
( )) ) (38)
48
( ))
)
)
(39)
This holds true for all with the exception of PB itself, which is an explanatory variable
in our Heckman model. For all other variables, the value
was solved in the previous model.
Therefore, the unconditional marginal effects of our Heckman model can also be interpreted as
percent changes in the expected benefit derived from the exempt status of retirement assets.
For PB, we expect a linear relationship between the benefit and the probability of filing, s
defined by equation 33, so we solve using the product rule:
( ))
)
(
)
(
) (
)
(40)
This approximates the change in benefits a change of 1 in the percent probability of filing
for bankruptcy. Since we solve for the unconditional marginal effect
from our Heckman
model, we will be able to solve for ( ))
and determine what portion of the full effect of PB on
the expected protection is attributable to sheltering. This portion will be evaluated at various
levels of our discrete variables for financial sophistication and education to conclude whether
individuals with higher levels of financial sophistication or education receive a greater portion of
the expected exemption benefit from sheltering.
6.4 Model Specification and Variable Selection
The variables chosen for this model were based in both our theoretical framework and the
literature. For each of the variables described below, how they were created and the underlying
data are discussed in Chapter 5. All data is derived from the SCF surveys from 2007 and 2010
from 10,900 households.
49
6.4.1 The Heckman Model Part 1
The first part of the Heckman model is specified as a probit model in Equations 19 and
20. Our dependent variable D is whether or not the individual has retirement assets, which has
an mean probability of 51.4%. The vector is composed of our explanatory variables, listed
here. First, we include the age of the household head, which we expect to be positively related to
D=1. Once an individual opens a retirement account, he will hold assets in the account until he
withdraws all of them. Very few individuals withdraw the entirety of their retirement assets
before retirement, and only a minority of retirees have depleted their retirement accounts
completely. The only other group with no retirement assets are those who have never opened an
account. This leads to our expectation that more individuals join the group who owns retirement
assets than those who deplete their assets, meaning a positive relationship between age and
owning a retirement asset.
Income, closely correlated to the ability to pay into an account, should be positively
related to owning a retirement asset. We include the natural log of income in the Z vector.
Similarly, our dummy variable for whether the individual is liquidity constrained should also
display a positive coefficient. Other dummy variables, including one for having access to an
employee-sponsored retirement plan and one variable for planning to retire soon are expected to
be positively related to D=1.
Demographic variables such as whether the household head is black, white, married, has
no children, one child, two children, or three or more children is included as well. Those
households with fewer children and those that contain a married couple should have a greater
probability of having a retirement plan.
50
The probability of filing for bankruptcy is included along with our dummy variables for
financial sophistication quintiles and whether the person has a bachelor’s degree, which
measures education. Financial sophistication and education measure the price of informational
barriers, and are hypothesized to be negatively related to price. Therefore, we expect that they
are positively related to holding retirement assets. We do not hypothesize any interaction effect
between PB and financial sophistication or education for the selection model. We expect that the
interaction effect between PB and those household measures will have a measurable effect on
those households who regularly consider retirement assets in their portfolio allocation decisions.
6.4.2 The Heckman Model Part 2
The second part of the Heckman model is specified as in Equation 22. Our variable Y
measures retirement assets in dollars, which are wildly and unevenly distributed in the upper few
percentiles of households. Because of the distribution of Y, we avoid hypothesizing a linear
relationship between Y and our independent variables, which are contained in the vector X.
Therefore, we use the natural log of total dollars, lnY, as our dependent variable.
The vector X contains many of the same variables as the vector Z in the first part of the
model. However, we include age squared along with age in the second part of this model
because the relationship between age and the level of retirement assets is complex. Based on the
life cycle theory discussed in Chapter 4, we expect that retirement assets steadily increase
throughout life until retirement, at which point they will decline. The variables for age and age
squared such capture this hyperbolic relationship.
The natural log of income, access to an employee retirement plan, planning to retire soon,
liquidity constrained status, and all our demographic variables are included in the second part of
the model, including variables for being black, white, married, having no children, one child, two
51
children, and three or more children. The coefficients on all the variables listed above are
expected to have the same signs as the first step of the model based on the same theoretical
relationships previously discussed. We also include a measure for the percent of retirement
plans that are allocated to risky assets to proxy for the expected returns associated with different
asset classes, such as stocks.
The measure of PB, the dummy variables for financial sophistication quintiles, and
education are included along with the following interaction terms: 1) PB and each financial
sophistication quintile dummy variables, and 2) PB and education. We expect a positive
coefficient on the latter interaction as well as the interaction for higher levels of financial
sophistication. These interaction terms will also help to add specificity to our marginal effect
calculations.
6.5 Other Model considerations
The computation of our Heckman model includes several considerations that will allow
for more accurate and reliable estimates. The first is a discussion of bootstrapping of our error
terms, and the second is the treatment of implicates for our data, which is derived from multiply
imputed survey results.
6.5.1 Bootstrapping
Bootstrapping was developed to correct for a number of problems associated with
uncertainty about the true distribution of the data (Efron 1979). The method operates by
resampling the data to estimate properties of variance, standard errors, and p-values. For our
model, we used 500 iterations with replacement to render our standard errors more accurate.
Ader, Mellenbergh, and Hand (2008) recommends the bootstrap procedure when the
theoretical distribution of a statistic is uncertain. For our data, one of our variables of interest,
52
the probability of filing for bankruptcy, was created from an estimated model. Thus, the true
value of this probability measure is uncertain, which affects the specification of our Heckman
model. Since bootstrapping is computed independent of the data distribution, it allows us to
indirectly assess the true variance and standard errors.
6.5.2 Imputation Adjustments
The Survey of Consumer Finances uses multiple imputation techniques that were
discussed in Chapter 5. Each household is represented by five observations per variable, and
missing responses are estimated using each of the five observations to capture the expected
distribution of responses from that household. For statistical inference, we use the Repeated-
Imputation Inference (RII) method to calculate the coefficients and standard errors. This
technique requires that we run a regression for each imputation of the data then compute our
parameters according to the calculations below. Here, Q represents the point estimate for a
single imputation, U is the variance within an imputation, B is the variance among imputations,
and T is the total variance. For our data which is imputed five times, according to Kennickell
(1998), the point estimates for our Heckman model are defined as simply
∑
(41)
To compute the standard errors of our estimates, we must compute U, B, and T first:
∑
(42)
∑ )
(43)
(44)
The standard error for our Heckman model is the square root of the total variance, √ .
53
Chapter 7: Results
The following results contains three parts: 1) the results from our Heckman model and
the marginal effects of the probability of filing for bankruptcy evaluated over different
subpopulations, 2) an estimate of the relative value of certain variables on the expected
protection offered by the bankruptcy exemption for retirement assets, and 3) a visual and
graphical representation of the expected level of retirement assets at different levels of the
probability of filing for bankruptcy. This will give way to a discussion of the results and
conclusions regarding our findings.
7.1 Model Parameters
7.1.1 Heckman Coefficients
Our Heckman model, specified in Chapter 6, solves for and by the respective two
parts. The results for the first stage is below establishing a relationship between our independent
variables and our model variable D, whether the household has retirement assets:
TABLE 5: Heckman Model Results, Part 1
Variable Name Coefficient Std. Error T-statistic P-value
HAVE RETIREMENT ASSETS
Age 0.003 0.001 2.516 0.012
Log Income 0.001 0.015 0.036 0.972
Access to Employee Retirement Plan 1.363 0.048 28.231 0.000
Retire Soon (<5 years) 0.101 0.089 1.130 0.259
Educated 0.051 0.041 1.232 0.218
Financial Sophistication
Quintile 4 0.352 0.068 5.139 0.000
Quintile 3 1.501 0.063 23.790 0.000
Quintile 2 2.452 0.070 35.245 0.000
54
Quintile 1 2.666 0.075 35.730 0.000
PB -0.004 0.001 -4.186 0.000
No Kids 0.072 0.067 1.072 0.284
1 Kid 0.063 0.071 0.890 0.374
2 Kids 0.102 0.072 1.420 0.156
Married 0.385 0.040 9.740 0.000
Black 0.132 0.072 1.832 0.067
White 0.235 0.051 4.594 0.000
Liquidity Constrained -0.047 0.044 -1.063 0.288
Constant -2.366 0.106 -22.244 0.000
The second part of our Heckman model defines the correlation between our independent
variables and the level of retirement assets in log dollars conditional on the household holding
greater than $0 in retirement assets:
TABLE 6: Heckman Model Results, Part 2
Variable Name Coefficient Std. Error T-statistic P-value
LOG RET ASSETS
Age 0.172 0.009 18.226 0.000
Age Squared -0.001 0.000 -13.169 0.000
Log Income 0.433 0.015 28.598 0.000
Access to Employee Retirement Plan 0.430 0.041 10.540 0.000
Retire Soon (<5 years) 0.122 0.070 1.738 0.082
Educated 0.596 0.044 13.477 0.000
Financial Sophistication
Quintile 4 0.395 0.254 1.551 0.121
Quintile 3 0.482 0.203 2.370 0.018
Quintile 2 0.974 0.200 4.867 0.000
Quintile 1 1.293 0.200 6.459 0.000
Interaction Terms
55
PB*Quintile 4 -0.007 0.024 -0.300 0.764
PB*Quintile 3 0.011 0.019 0.590 0.555
PB*Quintile 2 0.004 0.019 0.210 0.834
PB*Quintile 1 0.013 0.019 0.682 0.495
PB*Educated 0.004 0.003 1.145 0.252
PB -0.009 0.019 -0.458 0.647
No Kids 0.139 0.065 2.127 0.033
1 Kid -0.066 0.074 -0.891 0.373
2 Kids 0.092 0.069 1.324 0.185
Married 0.390 0.049 8.019 0.000
Black -0.124 0.102 -1.221 0.222
White 0.164 0.067 2.428 0.015
Risky Retirement Asset Percent 0.096 0.064 1.488 0.137
Liquidity Constrained -0.516 0.057 -9.122 0.000
Constant 1.417 0.336 4.214 0.000
The above results confirm our expectations about the direction of the relationship
between some of our independent variables and the level of retirement assets. All the financial
variables have an expected sign and reasonable magnitude. For example, our results demonstrate
that if income increases by 1%, the conditional expectation of our retirement assets increase by
.433%. Our demographic variables demonstrate weak relationships for those variables from
which we expected multiple competing effects, such has having children. Other variables with
clearer relationships, such as being married, demonstrate a positive relationship with log
retirement assets. The probability of filing for bankruptcy is significantly negatively related to
the selection into owning retirement assets, but displays no clear relationship with retirement
asset levels conditional on owning retirement assets. The marginal effects will demonstrate
whether this uncertain relationship holds true for all disaggregated population groups.
56
For our variables of interest, education and higher levels of financial sophistication are
significantly and positively related to the level of retirement assets. In the second stage of the
model, the interaction effects also demonstrated positive coefficients, but low levels of statistical
significance and relatively small magnitudes. This implies that the interaction terms may add
small amounts of information to our model specification, but does not imply that the marginal
effects of PB will be the same across financial sophistication quintiles or education levels. We
look to the marginal effects estimates to inform our expectation about the marginal effect of the
probability of filing on the level of retirement assets.
7.1.2 Marginal Effects
The following section reports the marginal effects of the probability of filing for
bankruptcy (measured by percent) on log retirement assets. First, we report the unconditional
marginal effects of PB for different groups:
TABLE 7: Unconditional Marginal Effects of PB by Subpopulation
Subpopulation lnY/ PB Std. Error T-statistic P-value
Financial Sophistication
Quintile 5 -0.0043 0.0013 -2.822 0.005
Quintile 4 -0.0103 0.0025 -3.296 0.001
Quintile 3 -0.0010 0.0038 -2.562 0.010
Quintile 2 -0.0053 0.0028 -3.277 0.001
Quintile 1 0.0041 0.0023 0.528 0.597
Education
No Bachelor’s Degree -0.0069 0.0021 -3.379 0.001
Bachelor’s Degree Holders -0.0032 0.0021 -1.471 0.141
57
The generally negative coefficients imply that being at high risk for bankruptcy might
cause an individual to allocate fewer resources to long-term savings in the form of retirement
assets. However, most of these marginal effects are not significantly different from zero.
Is the negative impact of an increase in probability of filing on retirement assets due to its
impact on selection into owning retirement assets, or does it also negatively influence the
retirement assets of those who do own them already? The answer cannot be addressed by the
unconditional marginal effects alone. Thus, we are interested in computing the probability
marginal effects and the conditional marginal effects for different subpopulations to determine
whether the negative relationship holds true after selection into owning retirement assets. The
following table provides probability marginal effects:
TABLE 8: Probability Marginal Effects of PB by Subpopulation
Subpopulation lnY/ PB Std. Error T-statistic P-value
Financial Sophistication
Quintile 5 -0.0004 0.0001 -4.009 0.000
Quintile 4 -0.0007 0.0002 -4.158 0.000
Quintile 3 -0.0013 0.0003 -4.225 0.000
Quintile 2 -0.0006 0.0002 -4.188 0.000
Quintile 1 -0.0005 0.0001 -4.144 0.000
Education
No Bachelor’s Degree -0.0007 0.0002 -4.209 0.000
Bachelor’s Degree Holders -0.0006 0.0001 -4.219 0.000
Table 8 demonstrates the uniformly negative impact of the probability of filing for
bankruptcy on selection into owning retirement assets, for all levels of financial sophistication
and education. The other component of marginal effects is the conditional marginal effects, for
those who have selected into owning retirement assets. This is presented below in Table 9.
58
TABLE 9: Conditional Marginal Effects of PB by Subpopulation
Subpopulation lnY/ PB Std. Error T-statistic P-value
Financial Sophistication
Quintile 5 -0.0080 0.0186 -0.432 0.666
Quintile 4 -0.0150 0.0138 -1.085 0.278
Quintile 3 0.0042 0.0042 0.981 0.327
Quintile 2 -0.0023 0.0025 -0.920 0.357
Quintile 1 0.0072 0.0020 3.575 0.000
Education
No Bachelor’s Degree -0.0057 0.0062 -0.912 0.362
Bachelor’s Degree Holders 0.0035 0.0020 1.751 0.080
This table demonstrates the resource allocation of those who already do own retirement
assets in response to an increase in the probability of filing for bankruptcy. Our expectation
about the positive relationship between retirement assets and the probability of filing for
bankruptcy holds true for only two categories of those who do already own retirement assets:
those with high levels of education and those who are most financially sophisticated. Only these
two conditional marginal effects are statistically significantly different than 0.
These results match our expectations about the probability of filing for bankruptcy and
informational costs. Although we highlight a significant benefit of retirement assets for all those
who have higher probabilities of filing for bankruptcy, the informational and compliance costs
are not hypothesized to be uniformly distributed. That is, access to information is inextricably
connected to taking advantage of the exemption protection, but differs across characteristic
groups.
Appendix A provides a graph for each level of financial sophistication and education to
explore the relationship between various levels of the probability of filing for bankruptcy and
59
retirement assets, all else constant. The y-axis is total dollars in the households quasi-liquid
retirement accounts, while the x-axis includes the probability of filing for bankruptcy.
Conditional and unconditional expectations are compared directly.
The graphs show a strongly negative relationship between PB and retirement assets for
those with lower levels of education and financial sophistication. Having higher levels of
education and financial sophistication tends to moderate this effect, especially for those who do
already possess retirement assets, that is, conditional on owning retirement assets. The positive
relationship with the greatest magnitude is clearly those in the highest level of financial
sophistication or a bachelor’s degree, conditional on already owning retirement assets.
7.2 Expected Benefit Calculations
7.2.1 Changes in PB
The above results demonstrate a change in portfolio allocation for select characteristic
groups in response to bankruptcy. However, our other measure of interest is the total effect of
the policy on those groups, of which the reallocation response is only a partial endogenous
effect. We refer to the relationship derived in Chapter 6.3,
( ))
(45)
Some information about the first term is found in Table 2. For the second term in
Equation 44 is defined as the impact of portfolio reallocation on the total benefit for a particular
individual or set of individuals resulting from the exempt status of retirement assets. For some
individuals, we cannot rule out the null hypothesis that
. If that null hypothesis is true,
hypothetically, then ( ))
is simply , with no additional impact of portfolio reallocation
for which to account.
60
For those who have a positive marginal effect of PB on log retirement assets, we compute
the relative magnitude of both and
, the two terms in the equation above.
The relative magnitudes will help us to understand what portion of the expected benefit of the
bankruptcy exemptions are due to portfolio reallocation. The following table defines these
percentages for the two groups that demonstrated a statistically significant positive relationship
between PB and log retirement assets: 1) those who are in the upper quintile of financial
sophistication and also possess retirement assets, and 2) those with a bachelor’s degree and also
possess retirement assets. Note that the derivation is evaluated at the disaggregated mean for the
subpopulation groups, including the mean for the probability of filing for bankruptcy.
TABLE 10: The Impact of Reallocation on Protected Assets
Subpopulation Total Effect Effect of
Reallocation Percent Impact of Reallocation
Financial Sophistication
Quintile 5, Has Retirement
Assets $2,816.14/ $80.28/ 2.85%
Bachelor’s Degree Holder,
Has Retirement Assets $2,540.94/ $53.52/ 2.11%
This table implies that the response to having a high probability of filing for bankruptcy
accounts for 2.85% and 2.11% of the total expected protection offered by bankruptcy exemptions
for retirement assets for our two respective groups. The total benefit is described in relative
terms, scaled by our constant which depends on the relative portion of Chapter 7 and Chapter
13 bankruptcies, as well as the dollar value of the benefit associated with an exempt asset in
Chapter 13 bankruptcy.
For all other subgroups, we cannot assume any relationship between the probability of
filing and retirement assets. Thus, the relative expected benefit due to a change in the probability
61
of filing for bankruptcy is simply the proportion of retirement assets. Chapter 5 provides these
weighted descriptive statistics disaggregated by financial sophistication and education.
7.2.2 Changes in Financial Sophistication and Education
The change in the expected benefit from bankruptcy exemptions for retirement assets was
defined in Chapter 6 as
( ))
(46)
The change in the percent of expected benefit is simply the unconditional marginal effect
of our Heckman model. Isolating the impact of an explanatory variable will reveal how much
expected financial gain can be attributable to changes in that variable, all else equal, with respect
to the bankruptcy exemption for retirement assets. The marginal effects of our variables of
interest, financial sophistication and education, are in the table below. The results answer the
question of how much better off would an individual be if he increased his financial
sophistication or education.
TABLE 11: Changes in Expected Benefit due to Changes in Financial Sophistication and
Education
Subpopulation lnY/ X Std. Error T-statistic Pvalue
Financial Sophistication
From Quintile 5 to Quintile 4 0.834 0.149 5.613 0.000
From Quintile 4 to Quintile 3 3.453 0.151 22.799 0.000
From Quintile 3 to Quintile 2 2.951 0.164 17.956 0.000
From Quintile 2 to Quintile 1 0.743 0.172 4.327 0.000
Education
From No Bachelor’s Degree to Bachelor’s
Degree 0.448 0.076 5.911 0.000
62
For each described changes above, the effect of an increase in financial sophistication and
education are both consistently positive on the expected benefit and statistically significant at the
99.9% confidence level. That is, our model confirms that those who are more sophisticated and
have higher education benefit significantly more from the bankruptcy exemption for retirement
assets than those who are less sophisticated and have lower levels of education respectively. We
can also identify the source of the differential: differences in the level of retirement assets. That
is, households that are more financially sophisticated and have more education benefit from the
bankruptcy exemption because they possess more retirement assets. We also note that part of
this differential is attributable to portfolio reallocation for those who do own retirement assets
and are at the highest levels of financial sophistication and education.
7.3 Graphical Representation
These differences can be seen in the following graphical representation of the
unconditional expected level of financial benefit at different levels of financial sophistication and
with different levels of probability of filing for bankruptcy. We use the following formula from
Chapter 6.3:
( ))
(
)
(47)
For changes in the percent probability of filing for bankruptcy, we approximate with the
following:
)| )|
( ))
|
(48)
where .
On the y-axis, we have an expected benefit measure, scaled by our constant
, and on the
x-axis, we measure various levels of the probability of filing for bankruptcy. Our graph
63
represents different characteristic groups, using the mean retirement asset level for the group.
These results are displayed in Appendix B.
We also represent the data in table form in Appendix C. Note that the benefits are
relative measures, and represent dollars scaled by our constant
. The results demonstrate a
dramatic differential among characteristic groups. Those who are more sophisticated or have
higher levels of education benefit a great deal more than those who are not in those groups for
the same levels of the probability of filing for bankruptcy. Especially, those who are educated
and those in the highest quintile of financial sophistication have the highest levels of expected
benefit.
It is also worth noting that the expected benefits would be perfectly linearly related to the
probability of filing for bankruptcy without the effect of portfolio reallocation. The slight
negative coefficients on most of our variables accounts for the diminishing rate of increase
across the x-axis. For those who are most financially sophisticated, the graph increases
exponentially, due to its positive unconditional marginal effect of PB. This effect accounts for a
portion of the differential across characteristic groups.
It is apparent from our estimation of the percent impact of financial sophistication and of
education on the expected protection change that the primary determinant of expected benefit is
the levels of retirement assets. The differences among groups in retirement assets explains most
of the variation in the expected benefit from the relevant bankruptcy exemption. It is also
noteworthy that based on our descriptive statistics in Chapter 5.3, the probability of filing for
bankruptcy is roughly even across all subgroups. In fact, those with lowest levels of financial
sophistication and education have slightly lower probabilities of filing. Having a higher
64
probability of filing, as demonstrated in the table above, is associated with greater expected
benefits from the bankruptcy exemptions for retirement assets.
65
Chapter 8: Conclusion
This chapter summarizes our findings from Chapter 7 and compares them to our
hypothesis and to the literature. We then discuss some limitations of the model and how this
research can be extended in the future to better understand behavior surrounding investment
before bankruptcy.
8.1 Important Findings
Our models demonstrate that the probability of filing for bankruptcy can impact the
savings level in a retirement account. Some individuals will respond to conditions of high
probability of filing by allocating fewer resources to a retirement account, while others will
allocate greater resources. Our results demonstrate which characteristics are related to this
response.
8.1.1 Portfolio Reallocation
Our theoretical framework highlighted the advantages of allocating resources to a
retirement account if one’s probability of filing for bankruptcy is high. However, we theorized
that there is significant informational or practical barriers to sheltering assets pre-bankruptcy.
We estimated that those with higher levels of education or financial sophistication will respond
differently to higher probabilities of filing for bankruptcy. Based on the marginal effects for our
Heckman model, the strongest evidence suggests that this is true, conditional on owning
retirement assets.
Using our statistically significant results only, we conclude that the probability of filing
for bankruptcy is positively related to retirement assets if two conditions are true: 1) the
household already owns retirement assets, and 2) the household head is either financially
sophisticated or has a bachelor’s degree. Our results, then, identify a determinant of a positive
66
marginal effect of the probability of filing for bankruptcy: self-selecting into owning retirement
assets. We infer that households with retirement assets tend to alter their behavior under new
conditions of bankruptcy. However, our results demonstrate that this effect does not necessarily
extend to those who do not own retirement assets. That is, we do not find strong evidence that
the probability of filing for bankruptcy predicts selection into a retirement asset.
These results are in line with our expectations and our hypothesis. For the first condition
in the paragraph above, an individual is more likely to have flexibility in optimizing his
retirement assets if he has self-selected into owning retirement assets. If an individual has no
retirement assets, we theorize that he has greater expected informational or financial barriers to
optimizing his portfolio for changes in a specific benefit. Even if the individual would, under
perfect information, respond to an increase in the probability of filing for bankruptcy by
increasing retirement asset allocation, he might lack the flexibility to do so. For the second
condition, education and financial sophistication also help the individual diminish these barriers
and protect his portfolio assets to a greater extent from bankruptcy risk.
8.1.2 Expected Benefits
The expected benefits of bankruptcy exemptions vary by individual based primarily on
the level of retirement assets and the probability of filing for bankruptcy. We find here that
financial sophistication and education significantly and strongly predict retirement asset levels.
Those with higher levels of financial sophistication and education have, on average, a higher
expected value associated with the exemption. That is, when the probability of filing for
bankruptcy increases, highly sophisticated or educated individuals receive much greater
protection.
67
Our model demonstrates that for those individuals who shelter assets in retirement
accounts in response to the probability of filing, sheltering compounds the expected benefits.
This sheltering effect, according to our results, benefits those in the highest quintile of financial
sophistication and those with a bachelor’s degree, both conditional on owning retirement assets.
Those two classes of individuals are those with the highest levels of expected protection. The
sheltering effect then helps those who are already extremely well protected. Similarly, the
negative marginal effect of the probability of filing for bankruptcy for other groups will diminish
their expected benefit.
In conclusion, we find evidence that the benefits associated with bankruptcy exemptions
for retirement assets are distributed heavily toward those with high financial sophistication and
education. Although the effect is small (less than 3 percent of the marginal expected benefit), the
sheltering effect helps redistribute even more benefits to those who are already most protected.
Section 8.2 below addresses the question concerning the origin of these benefits – that is, from
where are these benefits distributed – and the total distributional impact of bankruptcy
exemptions for retirement assets.
8.2 Limitations and Future Research
Expected benefits, as calculated here, do not account for expected costs. That is, the
benefits calculation takes into consideration the amount of retirement assets claimed in
bankruptcy as exempt, but not the impact on credit markets. Every dollar of exempt assets for a
debtor in bankruptcy is a dollar of lost revenue for creditors, resulting in profound changes in the
distribution, cost and quantity of credit via general equilibrium effects. This effect, which has
been documented throughout the literature, harms creditors and debtors alike. Some studies have
68
even suggested that the costs of these exemptions might outweigh the benefits, resulting in a net
loss in economic efficiency (Li and Sarte 2006).
Our results demonstrate the strong bias toward financially sophisticated and educated
individuals on the benefits side of retirement asset exemptions. Future research that examines
the distribution of costs will be useful in calculating the net benefits, rather than the gross
benefits, of the exemptions for retirement assets. Such a net benefit calculation will reveal
whether the uneven distribution of benefits holds true after accounting for costs.
Another limitation of our research is the measurement of expected benefits in non-dollar
terms. Our results are a relative measure, scaled by the constant , which is calculated based on
the benefits of exempt assets in Chapter 13 bankruptcy as well as the proportion of Chapter 13
filings against Chapter 7 filings. Instead, if was estimated, we could determine the dollar
benefits of the policy in absolute terms. Future research could estimate the instance of exempt
assets for Chapter 13 filers and even determine the factors related to the probability of filing for
each chapter. In the latter case, we could relax the assumption that is constant if the
probability of each chapter changes across the population. This would provide a more accurate
measure of the expected protection.
Another possible extension is to use individual bankruptcy data to further specify the
variable for the probability of filing for bankruptcy. The model we use draws primarily from
debt variables and no attitudinal variables or measures of financial sophistication (Domowitz
1999). If a respecification of that model included a measure of financial sophistication, we could
depart from our assumption that
) , which would add considerable
complexity to our model. If the relationship is positive, then we may be currently
overestimating the expected benefits of those with highest levels of financial sophistication.
69
8.3 Concluding Remarks
The research here makes a valuable contribution to the current literature. First, we have
demonstrated a method for evaluating the probability of filing for bankruptcy from the Survey of
Consumer Finances and using the measure as an explanatory variable. We have also provided
relevant calculations for evaluating an individual’s benefit with respect to bankruptcy
exemptions. These calculations can be used to help an individual correctly evaluate the benefits
of contributing to a retirement plan under varying financial conditions related to the probability
of filing for bankruptcy in the future.
Perhaps most importantly, we have continued the discussion regarding bankruptcy
exemptions as well as the effects of financial sophistication on the receipt of policy benefits. In
line with the current body of research, we have demonstrated the uneven impact of one aspect of
financial policy in the United States on different characteristic groups. Furthermore, we have
highlighted the potential relevance of financial sophistication in bankruptcy policy. We can infer
from the evidence here that financial sophistication continues to play a significant role in
accurately evaluating policy decisions in the United States.
70
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Appendix A: Expected Retirement Assets
Financial Sophistication – Quintile 5
Financial Sophistication – Quintile 4
0
5000
10000
15000
20000
25000
0 10 20 30 40 50 60 70 80 90 100
E(Y
)
PB
Unconditional
Conditional
0
10000
20000
30000
40000
50000
60000
70000
0 10 20 30 40 50 60 70 80 90 100
E(Y
)
PB
Unconditional
Conditional
74
Financial Sophistication – Quintile 3
Financial Sophistication – Quintile 2
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
0 10 20 30 40 50 60 70 80 90 100
E(Y
)
PB
Unconditional
Conditional
0
20000
40000
60000
80000
100000
120000
140000
160000
0 10 20 30 40 50 60 70 80 90 100
E(Y
)
PB
Unconditional
Conditional
75
Financial Sophistication – Quintile 1
Education – No Bachelor’s Degree
0
100000
200000
300000
400000
500000
600000
0 10 20 30 40 50 60 70 80 90 100
E(Y
)
PB
Unconditional
Conditional
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
0 10 20 30 40 50 60 70 80 90 100
E(Y
)
PB
Unconditional
Conditional
76
Education – Bachelor’s Degree
0
50000
100000
150000
200000
250000
300000
350000
400000
0 10 20 30 40 50 60 70 80 90 100
E(Y
)
PB
Unconditional
Conditional
77
Appendix B: Expected Benefits
Expected Benefits by Financial Sophistication
Expected Benefits by Education Level
0.00
50,000.00
100,000.00
150,000.00
200,000.00
250,000.00
300,000.00
0 10 20 30 40 50 60 70 80 90 100
E(B
)/μ
PB
Quintile 1
Quintile 2
Quintile 3
Quintile 4
Quintile 5
0.00
20,000.00
40,000.00
60,000.00
80,000.00
100,000.00
120,000.00
140,000.00
0
10
20
30
40
50
60
70
80
90
10
0
E(B
)/μ
PB
Bachelor's Degree
No Bachelor's Degree
78
Appendix C: Expected Relative Benefit Measures
Financial Sophistication Education
PB Quintile 5 Quintile 4 Quintile 3 Quintile 2 Quintile 1 No Bachelor's
Degree
Bachelor's
Degree
0 0.00 0.00 0.00 0.00 0.00 0 0 10 144.82 676.54 3,655.58 12,275.77 25,653.89 3,021.03 18,051.73 20 284.55 1,300.34 6,971.45 23,477.73 51,622.72 5,839.00 35,543.28 30 419.38 1,875.51 9,979.17 33,699.81 77,910.36 8,467.56 52,492.03 40 549.48 2,405.84 12,707.39 43,027.71 104,520.70 10,919.44 68,914.82 50 675.02 2,894.82 15,182.07 51,539.66 131,457.72 13,206.52 84,827.98 60 796.14 3,345.69 17,426.78 59,307.04 158,725.43 15,339.87 100,247.32 70 913.02 3,761.40 19,462.89 66,394.97 186,327.89 17,329.83 115,188.16 80 1,025.79 4,144.71 21,309.79 72,862.88 214,269.20 19,186.03 129,665.36 90 1,134.61 4,498.14 22,985.05 78,765.02 242,553.53 20,917.47 143,693.29 100 1,239.61 4,824.01 24,504.64 84,150.88 271,185.08 22,532.52 157,285.92